Mathematical Sciences: Models and Methodology for Positive Dependence

在积极依赖性和可靠性的框架内 理论，统计学中的一些主要研究课题， 应用概率模型。 这些措施包括： 发展衡量标准的统计应用， 置换的相关排序;（B）新的和更有效的 半序空间的保序回归算法; (c)不同类型的有序数据分析技术。 其他主题包括可靠性维护模型，模型 和随机长度多元正态数据的方法，以及 由非齐次Poisson产生的组合恒等式 流程. 这些主题的研究方法采用 结果和技术从积极的依赖，可靠性 理论和多元分析。 主要研究人员将探索一些 多元统计领域的理论课题 分析称为正相关，并考虑一些 这些理论成果的应用。 特别是 研究人员计划开发新的计算算法， 比目前的算法更有效。 这样做的目的 研究的目的是制定战略， 以最佳方式平衡维护成本和 崩溃的代价。

Within the framework of positive dependence and reliability theory, a number of major research topics in statistics and applied probability modeling are proposed. These include: (a) development of the statistical applications of metrics and related orderings on permutations; (b) new and more efficient isotonic regression algorithms for partially ordered spaces; and (c) various techniques for types of ordinal data analyses. Additional topics include reliability maintenance models, models and methodology for random length multivariate normal data, and combinatoric identities arising from nonhomogeneous Poisson processes. The research approaches to these topics employ results and techniques from positive dependence, reliability theory and multivariate analysis. The principal investigators will explore a number of theoretical topics in the area of multivariate statistical analysis called positive dependence and consider a number of applications of these theoretical results. In particular the investigators plan to develop new computational algorithms that are more efficient than current algorithms. The purpose of this research is to develop strategies for maintaining a system in an optimal fashion balancing the cost of maintenance against the cost of break-downs.